When you saw us outside building snow-mathematicians and throwing snowballs we weren't just larking about, honestly! We were actually conducting in-depth research into symmetry and trajectories — and here our results, behind door number 2...

To get you in the festive spirit Science in School is offering you an advent calendar with a difference — no little doors to open, no pictures of snowmen and no chocolate. Instead, each day for 24 days, they will send you an email with an inspiring teaching idea. Perhaps a science game to play at the end of term, maybe a fun experiment, some fascinating science facts, links to particularly good websites, or a beautiful picture to use in lessons.

What are continued fractions? How can they tell us what is the most irrational number? What are they good for and what unexpected properties do they possess? Where are they in the Universe and just what does chaos have to do with it? You can now watch John Barrow's lecture about the fascinating things you can uncover by writing numbers in this way.